非线性分数微分方程边值问题正解的存在性

数学季刊 ›› 2012, Vol. 27 ›› Issue (2): 293-300.

非线性分数微分方程边值问题正解的存在性

1. School of Mathematics, Jiaying University 2. School of Mathematical Science, South China Normal University

收稿日期:2010-12-03 出版日期:2012-06-30 发布日期:2023-03-31
作者简介:SONG Li-mei(1975-), female, native of Meizhou, Guangdong, a lecturer of Jiaying University, engages in ordinary diﬀerential equations.
基金资助:
Supported by the Research Fund for the Doctoral Program of High Education of China(20094407110001)； Supported by the NSF of Guangdong Province(10151063101000003)

Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Diﬀerential Equation

1. School of Mathematics, Jiaying University 2. School of Mathematical Science, South China Normal University

Received:2010-12-03 Online:2012-06-30 Published:2023-03-31
About author:SONG Li-mei(1975-), female, native of Meizhou, Guangdong, a lecturer of Jiaying University, engages in ordinary diﬀerential equations.
Supported by:
Supported by the Research Fund for the Doctoral Program of High Education of China(20094407110001)； Supported by the NSF of Guangdong Province(10151063101000003)

摘要/Abstract

摘要： In this paper, we study a Dirichlet-type boundary value problem (BVP) of nonlinear fractional differential equation with an order α∈(3,4], where the fractional derivative D^α_o+is the standard Riemann-Liouville fractional derivative. By constructing the Green function and investigating its properties, we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP. The Krasnosel’skii fixed-point theorem in cones is used here. We also give an example to illustrate the applicability of our results.

关键词: fractional differential equation, boundary value problem, positive solution; fractional Green function, fixed-point theorem in cones

Abstract: In this paper, we study a Dirichlet-type boundary value problem (BVP) of nonlinear fractional differential equation with an order α∈(3,4], where the fractional derivative D^α_o+ is the standard Riemann-Liouville fractional derivative. By constructing the Green function and investigating its properties, we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP. The Krasnosel’skii fixed-point theorem in cones is used here. We also give an example to illustrate the applicability of our results.

Key words: fractional differential equation, boundary value problem, positive solution; fractional Green function, fixed-point theorem in cones

中图分类号:

O175.8

宋利梅, 翁佩查. 非线性分数微分方程边值问题正解的存在性[J]. 数学季刊, 2012, 27(2): 293-300.

SONG Li-mei, WENG Pei-xuan. Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Diﬀerential Equation[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(2): 293-300.

[1]	王川, 乔炎. Korteweg-de Vries方程的Legendre时空谱配置方法[J]. 数学季刊, 2023, 38(4): 392-400.
[2]	张宏伟, 李栋浩, 呼青英. 具非局部非线性阻尼和源项的波方程解的能量衰减估计[J]. 数学季刊, 2020, 35(3): 302-310.
[3]	漆勇方, 韩丽涛, 魏胥婷. 具有多个单项式的分数阶微分系统的李雅普诺夫型不等式的研究[J]. 数学季刊, 2018, 33(3): 293-301.
[4]	滕南, 马扶博, 于童, 莫冉. 时间测度上奇异高阶两点边值问题解的存在性与唯一性[J]. 数学季刊, 2017, 32(1): 49-58.
[5]	吴红萍. 非线性奇异二阶三点边值问题的对称正解[J]. 数学季刊, 2015, 30(3): 358-365.
[6]	张林丽, 刘安平, 刘伟安. 二阶脉冲积分微分方程周期边值问题[J]. 数学季刊, 2015, 30(2): 227-235.
[7]	谭惠轩, 封汉颍, 冯杏芳, 杜亚涛. 带p-Laplacian算子的三阶三点边值问题的三个正解[J]. 数学季刊, 2015, 30(1): 55-65.
[8]	韩仁基, 周先锋, 李翔, 蒋威. 一类非线性分数阶泛函微分方程脉冲边值问题的解[J]. 数学季刊, 2014, 29(3): 400-411.
[9]	张豫川, 周宗福. 带有p-Laplacian算子的四阶时滞微分方程边值问题的正解[J]. 数学季刊, 2014, 29(2): 171-179.
[10]	李耀红. 无穷区间上具积分边值条件的二阶非线性奇异微分方程组正解存在性[J]. 数学季刊, 2014, 29(1): 55-64.
[11]	李平润. 某些类具有反射与平移移位的卷积型奇异积分方程的解法[J]. 数学季刊, 2014, 29(1): 107-115.
[12]	孙林林, 梁铁旺, 张建朋. 带有非齐次温度边界的一维可压缩粘性微极流体模型的局部正则性[J]. 数学季刊, 2014, 29(1): 129-141.
[13]	宋志华. 非线性Kirchhoff型波动方程解的能量衰减[J]. 数学季刊, 2013, 28(4): 485-491.
[14]	张豫川, 周宗福, 徐鑫. 一类三阶非线性微分方程耦合系统边值问题的正解[J]. 数学季刊, 2013, 28(4): 522-531.
[15]	赵霞, 胡卫敏, 蒋达清. 具P-Laplacian算子的二阶微分系统奇异边值问题正解的存在性[J]. 数学季刊, 2013, 28(3): 345-354.